% Источник: NEERC Northern QF 2004, problem C

\begin{problem}{Collecting Bugs}
{collect.in}{collect.out}
{0.5 секунд}{64 мегабайта}{}

Ivan is fond of collecting. Unlike other people who collect post stamps, coins or other material stuff, he
collects software bugs. When Ivan gets a new program, he classifies all possible bugs into $n$ categories.
Each day he discovers exactly one bug in the program and adds information about it and its category
into a spreadsheet. When he finds bugs in all bug categories, he calls the program disgusting, publishes
this spreadsheet on his home page, and forgets completely about the program.
Two companies, Macrosoft and Microhard are in tight competition. Microhard wants to decrease sales
of one Macrosoft program. They hire Ivan to prove that the program in question is disgusting. However,
Ivan has a complicated problem. This new program has $s$ subcomponents, and finding bugs of all types
in each subcomponent would take too long before the target could be reached. So Ivan and Microhard
agreed to use a simpler criteria — Ivan should find at least one bug in each subsystem and at least one
bug of each category.
Macrosoft knows about these plans and it wants to estimate the time that is required for Ivan to call its
program disgusting. It’s important because the company releases a new version soon, so it can correct
its plans and release it quicker. Nobody would be interested in Ivan’s opinion about the reliability of the
obsolete version.
A bug found in the program can be of any category with equal probability. Similarly, the bug can be
found in any given subsystem with equal probability. Any particular bug cannot belong to two different
categories or happen simultaneously in two different subsystems. The number of bugs in the program
is almost infinite, so the probability of finding a new bug of some category in some subsystem does not
reduce after finding any number of bugs of that category in that subsystem.
Find an average time (in days of Ivan’s work) required to name the program disgusting.

\InputFile

Input file contains two integer numbers, $n$ and $s$ ($0 < n, s \le 1\,000$).

\OutputFile

Output the expectation of the Ivan’s working days needed to call the program disgusting, accurate to 4
digits after the decimal point.

\Example

\begin{example}
\exmp{
1 2
}{
3.000000
}%
\end{example}

\end{problem}
